This thesis considers the design of distributed state and output feedback control algorithms for linear multi-agent systems with performance guarantees in the presence of delays. The multi-agent systems considered are assumed to exchange relative information over an information network. As a first contribution, a novel distributed state feedback control design method with a sub-optimal LQR performance is developed for a network of multiple agents. For the control design process, it is assumed that the exchange of relative information is instantaneous. A stability analysis of the proposed control law is performed by incorporating delays in relative information to ascertain the maximum possible delay that can be accommodated by the communication network.
Subsequently, the assumption of the exchange of instantaneous relative information in the control design process is relaxed and the relative information is assumed to be delayed. The system is then represented as a time-delay system. Distributed state feedback control synthesis methods are then developed for the system with a certain level of LQR performance. In the above contributions, the time delay analysis and the development of delay based control methods, it is implicitly assumed that delays are detrimental to achieving cooperative tasks for a multi-agent system. Subsequently, positive effects of delays in communication of relative information are explored. For this a network of vehicles described by double integrator dynamics, which cannot be stabilized by static output feedback without delays, is considered. A novel control design method to achieve exponential stabilization of such a multi-agent system by static output feedback using delayed relative information is developed. Conclusions are drawn from the results of the research presented in this thesis and a few directions for future work are identified.